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The Rallis-Schiffmann lifting and Arthur packets of \(G_2\). (English) Zbl 1107.11025

This paper is an announcement of results that refine those of S. Rallis and G. Schiffmann [Theta correspondence associated with \(G_2\), Am. J. Math. 111, No. 5, 801–849 (1989; Zbl 0723.11026)]. In that paper the authors construct a theta lift from representations of the double cover of \(\mathrm{SL}_2\) to a group of type \(\mathrm{G}_2\). As usual this consists of two parts, one local, the other global. They analyse the local correspondence in detail with sketches of proofs. They then show how this can be used to determine the image of the global correspondence.

MSC:

11F70 Representation-theoretic methods; automorphic representations over local and global fields
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings

Citations:

Zbl 0723.11026
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